Normal operators in algebras without nice approximants
Authors:
Don Hadwin and Terry A. Loring
Journal:
Proc. Amer. Math. Soc. 125 (1997), 159161
MSC (1991):
Primary 46L80, 47A58; Secondary 46L05, 47C15
MathSciNet review:
1371125
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Abstract: The second author constructed a separable direct limit algebra with real rank zero containing a normal element whose spectrum is the closed unit disk that is not the limit of normal elements in the limiting algebras, and is not a limit of normals in the algebra having finite spectrum. We use Fredholm index theory to modify and simplify this construction to obtain such examples that are not limits of any ``nice'' types of elements.
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Additional Information
Don Hadwin
Affiliation:
Department of Mathematics, University of New Hampshire, Durham, New Hampshire 03824
Email:
don@math.unh.edu
Terry A. Loring
Affiliation:
Department of Mathematics and Statistics, University of New Mexico, Albuquerque, New Mexico 87131
Email:
loring@deepthought.unm.edu
DOI:
http://dx.doi.org/10.1090/S0002993997037349
PII:
S 00029939(97)037349
Received by editor(s):
July 3, 1995
Communicated by:
Palle E. T. Jorgensen
Article copyright:
© Copyright 1997
American Mathematical Society
